Time dependent correlations of inflationary perturbations

– We show that if the primordial classical perturbations were generated by the gravitational particle creation during inflation, and followed by an evolution of quantum-to-classical transition , the time dependent correlation of these perturbations is long-tailed with a correlation time larger than the Hubble-time. Consequently, the inflationary perturbations are locally scale-scale correlated. Hence, the interaction of the fields during inflation can be explored via the detection of the local scale-scale correlation of the CMB fluctuations. It is fundamentally important to understand the nature of the primordial cosmological perturbations which are responsible for the formation of structures that we see today. The inflation paradigm for the early universe assumes that the cosmic perturbations are initiated by the process of particle creation from vacuum in the background gravitational field of the expanding universe [1]. The subsequent decoherence of the quantum fluctuations leads to a quantum-to-classical transition [2], and gives rise to the initial perturbations in the radiation dominated era on scales beyond the Hubble radius. Therefore, the earliest evolution of the inflationary cosmological fluctuations is governed by the gravitational particle creation accompanying the quantum-to-classical transition. Recently, the mechanism of the gravita-tional particle creation is re-emphasized with the development of the quintessential inflation model [3]. However, it still seems to lack some testable predictions of these mechanisms. In this Letter, we will show that the time-dependent correlation of the primordial perturbations is one of such testable predictions. In the " standard " inflation, i.e. the slow-roll inflation caused by a single scalar inflaton φ, the correlation time of the primordial perturbations is longer than the Hubble time H −1. This correlation will entail a non-trivial observable feature – the local scale-scale correlation of the initial perturbations. The time-dependence of cosmological perturbations is generally not observable in non-inflationary models, because the observed mass field does not contain two or multi-time information of the perturbations. In contrast, the inflationary scenario provides an excellent prospect to observing the time-dependence of the initial perturbations in a given region on the scale of horizon. Owing to the so-called " first out – last in " feature, a fluctuation crossing over the Hubble radius H −1 at the moment t × will yield a perturbation at the end of the inflation, t f , with the physical wavenumber given by [4]